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Quantitative Reasoning

The following paragraphs will separate the results obtained after employing descriptive statistic tools to the pair of observations.
These tools figure out the mean and the median percentage of smokers in the population, distinguished on the basis of gender. Mode has been ignored in this respect since it is irrelevant to figure out the maximum percentage to assess the average characteristics.
The mean as well as the median percentage of smokers is lower for females than for males. An obvious implication from the same is that males are more inclined towards smoking than their female counterparts. Here mean is the weighted average implying approximately 19% and 27% of the female and male populations in any nation to be regular smokers, respectively. On the other hand, the median value indicates that among all nations taken collectively, in half of the cases, more than 18.9% of the females are found to smoke, in contrast to 24% among the males (Gravetter & Wallnau, 2008).
Measures of dispersion indicate the degree to which the observations are scattered around the mean value. The higher the value of the measure, greater will be the dispersion about the mean and thus, the applicability of the mean value as a core feature of the population will be disturbed. Significance of standard deviation is almost equivalent to that of variance given that the former is the positive square root of the latter.
The percentage of female smokers distributed among various groups in the entire population differs from the mean value so calculated, though it is lower than the degree of dispersion of the male smokers. The variance and standard deviation statistics yield that percentage of male smokers in some nations is much higher as well as lower than the mean percentage of male smokers so calculated. However, similar statistics for females rule out such extremeness.
The adjoining diagram compares the percentage of male and female smokers in the entire ...Show more


Descriptive statistics help a researcher to analyse the basic characteristics or features of a set of observations underlying a variable (Healey & Prus, 2009). Central Tendency and Measures of Dispersion could be considered as two sections of the subject primarily targeted…
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